High-Temperature Gibbs States are Unentangled and Efficiently Preparable
CoRR(2024)
摘要
We show that thermal states of local Hamiltonians are separable above a
constant temperature. Specifically, for a local Hamiltonian H on a graph with
degree 𝔡, its Gibbs state at inverse temperature β, denoted
by ρ =e^-β H/ tr(e^-β H), is a classical distribution
over product states for all β < 1/(c𝔡), where c is a
constant. This sudden death of thermal entanglement upends conventional wisdom
about the presence of short-range quantum correlations in Gibbs states.
Moreover, we show that we can efficiently sample from the distribution over
product states. In particular, for any β < 1/( c 𝔡^3), we can
prepare a state ϵ-close to ρ in trace distance with a depth-one
quantum circuit and poly(n) log(1/ϵ) classical overhead. A
priori the task of preparing a Gibbs state is a natural candidate for achieving
super-polynomial quantum speedups, but our results rule out this possibility
above a fixed constant temperature.
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